Question

Find the equation of locus of a point which in equidistant from the coordinate axes.

Answer 1

Let $P(h,k)$ be any point in the locus.

Let $PM$ be the perpendicular distance of $P$ fro $x$-axis, i.e.,

$PM=\left|x\right|$

Let $PNeft$ be the perpendicular distance of $P$ fro $y$-axis, i.e.,

$PN=\left|y\right|$

$\because PM=PN\left(\text{Given}\right)$

$\Rightarrow \left|x\right|=\left|y\right|$

Squaring both sides, we have

$x^2=y^2$

$\Rightarrow x^2-y^2=0$.

Thus, locus of $P$ is $x^2-y^2=0$.